Generally, NOx (Nitrogen Oxides) contained in exhaust gas of an internal combustion engine is purified in reaction of the NOx with a reducing agent in the presence of a reducing catalyst. For example, a Patent Literature (JP 2009-162173 A) discloses a purifying system that uses fuel (hydrocarbon compound) for combustion of an internal combustion engine as a reducing agent, and the system supplies the fuel into an exhaust passage at a position upstream of a reducing catalyst. In the purifying system, when a temperature of the reducing catalyst does not reach an activation temperature, fuel supply is stopped until the temperature of the reducing catalyst reaches the activation temperature.